Advice please!

My husbands ex popped up as she likes to do! Back story. . .We broke up in 2016 about 5 months after our daughter was born (this was before we were married) and he started dealing with her (someone he told me not to worry about while dating). Anyways, we got back together after a year, but this girl loves to pop up like once a year and i blame him because he used to allow it & entertain her in my opinion. We got married last year and we now have another baby on the way and things have been great between us. I really see the change in us both I mean we’re young 25 we started dating at 14 so we’ve grown and learned from our mistakes together! Well this girl decided to pop up again. She texted him at 1:30 in the morning (so inappropriate knowing he’s not only in a relationship but married with a baby on the way). He called the number and discovered it was her. He asked her how she got his number and she claimed it was in her gmail attached to my name (which would make since because our phones and service are in my name) but that was the first thing that didn’t make sense to me because if it was under my name how did you know it was him and not me? So she preceded to tell him she just wanted to apologize for the past and that she’s trying to right her wrongs! He cut the conversation short told her okay thanks bye. I wasn’t around him for the conversation this is what he told me because he works 3rd shift he was at work when she pulled this. That was the second thing that was off to me if she wanted to right her wrongs why would she text a married man at 1 in the morning! He told me everything and I respect that because he could have deleted the messages and the call and act like nothing happened but he came to me and told me about it! My thing is where do we go from here? I feel like instead of just cutting the conversation short he should have made it very clear to her that her actions were inappropriate and she needs to not contact him anymore. He said he was thrown off because he doesn’t even know how she got his number and that none of this adds up to him and I am thinking the same! I do not feel her intentions are good I think she thought she was texting me and she was going to get him in trouble! He says he’ll do anything to prove to me he wants nothing to do with this girl but my thing is idk what to tell him to do it would be pointless to reach out now and say hey what you did was not cool don’t contact me anymore. I feel like the moment to say that would’ve been during that call. Should I just let it go or should we dead this situation once and for all?? I just don’t want her popping up anymore I’m so over it. I hope this made sense I’m trying to sum up years worth of drama lol.